F?rster Energy Transport in Metal-Organic Frameworks Is beyond Step-by-Step Hopping

Article abstract of DOI:10.1021/jacs.6b01345

Metal-organic frameworks (MOFs) with light-harvesting building blocks designed to mimic photosynthetic chromophore arrays in green plants provide an excellent platform to study exciton transport in networks with well-defined structures. A step-by-step exciton random hopping model made of the elementary steps of energy transfer between only the nearest neighbors is usually used to describe the transport dynamics. Although such a nearest neighbor approximation is valid in describing the energy transfer of triplet states via the Dexter mechanism, we found it inadequate in evaluating singlet exciton migration that occurs through the F?rster mechanism, which involves one-step jumping over longer distance. We measured migration rates of singlet excitons on two MOFs constructed from truxene-derived ligands and zinc nodes, by monitoring energy transfer from the MOF skeleton to a coumarin probe in the MOF cavity. The diffusivities of the excitons on the frameworks were determined to be 1.8 × 10^-2 cm²/s and 2.3 × 10^-2 cm²/s, corresponding to migration distances of 43 and 48 nm within their lifetimes, respectively. "Through space" energy-jumping beyond nearest neighbor accounts for up to 67% of the energy transfer rates. This finding presents a new perspective in the design and understanding of highly efficient energy transport networks for singlet excited states.

Full text of DOI:10.1021/jacs.6b01345

Subscriber access provided by ORTA DOGU TEKNIK UNIVERSITESI KUTUPHANESI
Article
Förster Energy Transport in Metal-Organic
Frameworks Is Beyond Step-by-Step Hopping
Qiongqiong Zhang, Cankun Zhang, Lingyun Cao, Zi Wang, Bing An,
Zekai Lin, Ruiyun Huang, Zhiming Zhang, Cheng Wang, and Wenbin Lin
J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.6b01345 • Publication Date (Web): 25 Mar 2016
Downloaded from http://pubs.acs.org on March 26, 2016
Just Accepted
“Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted
online prior to technical editing, formatting for publication and author proofing. The American Chemical
Society provides “Just Accepted” as a free service to the research community to expedite the
dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts
appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been
fully peer reviewed, but should not be considered the official version of record. They are accessible to all
readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered
to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published
in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just
Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor
changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers
and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors
or consequences arising from the use of information contained in these “Just Accepted” manuscripts.
Journal of the American Chemical Society is published by the American Chemical
Society. 1155 Sixteenth Street N.W., Washington, DC 20036
Published by American Chemical Society. Copyright © American Chemical Society.
However, no copyright claim is made to original U.S. Government works, or works
produced by employees of any Commonwealth realm Crown government in the course
of their duties.

Page 1 of 8
Journal of the American Chemical Society
1
2
3
4
5
6
7
8
9
Förster Energy Transport in Metal-Organic Frameworks Is Be-
yond Step-by-Step Hopping
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Qiongqiong Zhang[a] †, Cankun Zhang[a] †, Lingyun Cao[a] †, Zi Wang[a], Bing An[a], Zekai Lin[b], Ruiyun
Huang[a], Zhiming Zhang[a] ‡, Cheng Wang[a] *, and Wenbin Lin[a],[b]
[a] Collaborative Innovation Center of Chemistry for Energy Materials, State Key Laboratory of Physical Chemistry of Solid
Surfaces, Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005,
P.R. China
[b] Department of Chemistry, University of Chicago, 929 E 57th Street, Chicago, IL 60637, USA
Supporting Information Placeholder
Exciton dynamics on MOF networks have been described as a
step-by-step random hopping, which comprises elementary steps
of energy transfer between adjacent ligands.37,40 We adopted this
understanding of nearest-neighbor hopping (NNH) in our previous
studies on efficient energy transport of triplet-states in a series of
ABSTRACT: Metal-organic frameworks (MOFs) with light-
harvesting building blocks designed to mimic photosynthetic
chromophore arrays in green plants provide an excellent platform
to study exciton transport in networks with well-defined structures.
A step-by-step exciton random hopping model made of the ele-
mentary steps of energy transfer between only the nearest neigh-
bors is usually used to describe the transport dynamics. Although
such a nearest neighbor approximation is valid in describing the
energy transfer of triplet states via the Dexter mechanism, we
found it inadequate in evaluating singlet exciton migration that
occurs through the Förster mechanism, which involves one-step
jumping over longer distance. We measured migration rates of
singlet excitons on two MOFs constructed from truxene-derived
ligands and zinc nodes, by monitoring energy transfer from the
MOF skeleton to a coumarin probe in the MOF cavity. The diffu-
sivities of the excitons on the frameworks were determined to be
1.8×10-2 cm2/s and 2.3×10-2 cm2/s, corresponding to migration
distances of 43 nm and 48 nm within their lifetimes, respectively.
“Through space” energy-jumping beyond nearest neighbor ac-
counts for up to 67% of the energy transfer rates. This finding
presents a new perspective in the design and understanding of
highly efficient energy transport networks for singlet excited
states.
2+
2+ 41,52
MOFs containing Ru(bpy)3 and Os(bpy)3
.
The nearest-
neighbor approximation was confirmed by the short energy trans-
fer distance of triplet 3MLCT states mainly via the Dexter mecha-
nism, which requires wave-function overlap between the donor
and the acceptor. This simple successive hopping model also de-
scribes singlet exciton dynamics in porphyrin-based MOFs.40
However, the model cannot fully describe Förster-type singlet
exciton dynamics due to the involvement of the “through-space”
jumping beyond nearest neighbors. Recent reports of Förster en-
ergy transfer between dopants in single steps over long distances
in MOFs suggest the importance of including jumping beyond
nearest neighbors (JBNN, Fig. 1).45,46
In this work, we studied Förster energy transport of singlet ex-
citons in two light-harvesting MOFs with truxene-based ligands.
We found that the step-by-step NNH model was inadequate for
quantifying our experimental observations because JBNN ac-
counted for up to 67 % of migration rates in our systems.
Introduction
Natural photosynthesis begins by efficiently funneling energy
collected from sunlight to reaction centers via exciton transport.1,2
To study this process, exciton migrations over long distances have
been explored in artificial networks3-15 such as light-harvesting
metal-organic frameworks (MOFs).16-20 As a structurally well-
defined platform,21-24 MOFs not only present new opportunities
for the judicious design of antenna materials using chromophore-
based ligands,25-36 but also enable study of energy transport dy-
namics in networks with well-defined structures.37-46 The chro-
mophores can be isolated from each other on the MOF skeleton
with inter-chromophore distances of usually 1-2 nm, a value very
close to that in natural photosynthetic membranes (e. g. inter-
chlorophyll distances are 1-1.3 nm in chloroplasts).47-49 This lig-
and separation in space leads to energy transfer in a weak elec-
tronic coupling regime, in contrast to molecular crystals with
direct close packing and strong electronic coupling. MOF crystals
are thus extremely favorable crystalline models for photosynthetic
antenna arrays in green plants and photosynthetic bacteria.50,51
Figure 1. Cartoon showing two distinct pathways in exciton mi-
gration on a network of chromophores: 1) Step-by-step nearest
neighbor hopping (NNH); 2) Long-distance jumping. The exciton
can diffuse on the network and get transferred to acceptor mole-
cules (e.g., reaction centers in photosynthesis) jumping beyond
nearest neighbors (JBNN) in the network.
ACS Paragon Plus Environment

Journal of the American Chemical Society
Page 2 of 8
Exciton migration was monitored by employing coumarin dye
Figure 2. Structures of truMOF-1 and truMOF-2. The green
molecules in the MOF cavity as an emissive observer.6 Excitons
move around the MOF skeleton via ligand-to-ligand energy ex-
change until they find a coumarin, after which the energy is trans-
ferred to the dye. The more mobile the exciton, the greater the
likelihood it will end up on a dye molecule within its emission
lifetime. Truxene ligands correspond to the antenna array for
light-harvesting in natural photosynthetic systems, and coumarin
dyes correspond to reaction centers that accept the excitons. The
emission ratio between the coumarin dye and the ligands thus
serves as a sensitive measurement of exciton migration rates. We
found the exciton diffusivities on the two MOF skeletons to be
1.8×10-2 cm2/s and 2.3×10-2 cm2/s, which correspond to migration
distances of 43 nm and 48 nm within their lifetimes, respectively.
triblade represents the truxene ligand with C3h symmetry and the
red dots represent the Zn10 and Zn4 SBUs in truMOF-1 and -2,
respectively.
1
2
3
4
5
6
7
8
Dye Loading
Coumarin dye molecules were loaded into the porous MOFs by
a solution impregnation method. The crystals were equilibrated
with EtOH solutions of coumarin 343 for 48 hours, followed by
briefly washing away the dye molecules on the external surface of
the crystal with fresh solvent. The dye loading percentage was
quantified by combined fluorescence and UV-Vis measurements
of digested DMF solution of dye@MOF hybrids, and can be fine-
tuned by using coumarin solutions of different dye concentrations
for loading (see Fig. S10-18). The dye loading level expressed as
coumarin dye / MOF ligand ratio ranges from 0% to 2.1% in the
experiments. These doping levels are close to the ratio (0.45~5%)
between reaction centers and light-harvesting chlorophylls in the
photosynthetic system of green plants.47,53-55
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Results and Discussion
MOF Synthesis and Structural Characterization
The two MOFs in our study (truMOF-1 and truMOF-2) were
constructed from truxene-tribenzoate ligands (5, 5΄, 10, 10΄, 15,
15΄ -hexaethyltruxene-2,7,12–tri-benzoic acid = H3L, see Scheme
S1 and Fig. S1-3 in supporting information [SI]) and Zn10(μ4-
O)4(carboxylate)12 or Zn4(μ4-O)(OH)3(OH2)3(carboxylate)3 sec-
ondary building units (SBUs) as shown in Fig. 2. Their structures
were determined by single crystal X-ray diffraction studies (see
Table S1&2; see Fig. S4&5 for powder X-ray diffraction patterns
and Fig. S6-9 for chemical composition determination). Both
MOFs crystallize in the cubic crystal system, with the space group
The positions of adsorbed dye molecules were estimated from
molecular dynamic calculations (see the following sections). The
dye configurations with lowest energies were plotted in Fig. S19.
The coumarin dye molecule in truMOF-1 adheres to one of the
benzene rings of a truxene ligand, and sits in the valley formed by
two adjacent truxene ligands and the SBU. In truMOF-2, the dye
molecule is in close contact with three adjacent truxene ligands
and sits in a bowl formed by the three ligands.
̅
of 퐹43푚 for truMOF-1 and I213 for truMOF-2. In truMOF-1,
four of the triangular L ligands form a tetrahedral cage and the
cages are further linked to each other on the vertex through the
SBUs to give a net of ttt topology and a framework formula of
Zn10(μ4-O)4(L)4. The center-to-center distance between adjacent
ligands in the same cage is 0.87 nm, while distances between
cages are larger with the shortest ligand-to-ligand distance of 1.8
nm. In truMOF-2, the L ligands with the C3h symmetry and the 3-
connected SBUs link to each other alternately to give two-fold
interpenetrated 3,3-connected nets of srs topology and a frame-
work formula of Zn4(μ4-O)(OH)3(OH2)3(L). Each ligand has three
nearest neighbors on the interpenetrated net with a ligand-to-
ligand distance of 1.3 nm. Both MOFs possess 3D-connected
channels with pore sizes of 2.2 nm for truMOF-1 and 1.7 nm for
truMOF-2. The high cubic symmetry of the crystals together with
the random orientations of transition dipoles due to the C3h sym-
metry of the ligands lead to macroscopically isotropic exciton
transport dynamics without the usual complication from crystal
anisotropy.
Figure 3. (a) Scheme showing the energy transfer from the trux-
ene ligand on the MOF to the coumarin dye. (b) Excita-
tion/absorption and emission spectra of the ligand in MOF and the
dye molecule in DMF.
Fluorescence Measurement and Energy Transfer Efficiency
The overlap of the coumarin absorption and ligand L emission
spectra as shown in Fig. 3 suggests possible efficient energy trans-
fer from the ligand to the dye. The steady state emissions of the
dye@MOFs confirmed such transfer. Upon excitation at the lig-
and absorption wavelength of 370 nm,56 two emission peaks ap-
peared in the spectra, corresponding to the emission of the L lig-
and (max = 395 nm) and the emission of dye resulting from ener-
gy transfer (max = 485nm). This energy transfer can also be veri-
fied by the excitation spectra monitored at the dye emission max-
imum at 485 nm, which showed two excitation peaks correspond-
ing to direct excitation of the dye (max= 445 nm) and excitation
of the ligand (max= 370 nm) followed by energy transfer to the
dye (Fig. 4a). All the fluorescence measurements in this work
were performed at room temperature.
ACS Paragon Plus Environment

Page 3 of 8
Journal of the American Chemical Society
peak almost disappears, corresponding to close to unity energy
1
2
3
4
5
6
7
8
transfer efficiency. The ratios between the integrated intensities of
the dye and the ligand (Idye/Iligand) at the excitation wavelength of
ligand absorption serve as a figure of merit to evaluate the degree
of energy transfer (Fig. 4c&d). These data, together with the
simulated values from different models, suggest significant con-
tribution of exciton jumping beyond nearest neighbors (see the
following sections). An Idye/Iligand value as high as 57 was obtained
for truMOF-1 with a dye loading level of 2.1%, corresponding to
energy transfer efficiency of 98% as calculated by
9
I푑푦푒/I푙푖푔푎푛푑
Efficiency =
10
11
12
13
14
15
16
I푑푦푒
+ QY푑푦푒/QY푙푖푔푎푛푑
I푙푖푔푎푛푑
where QY stands for quantum yield (Fig. S20&21). TruMOF-2
shows even more efficient energy transfer with an Idye/Iligand value
of 72 at a dye loading level of 1.8%.
Figure 4. a) Emission spectra of dye@truMOF-1 with excitation
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
at 370 nm and excitation spectra of dye@truMOF-1 monitored at
the emission wavelength of 485 nm b) Emission spectra of
dye@truMOF-2 with excitation at 370 nm, with dye loading lev-
els of 0% (red), 0.12% (black), 0.32% (blue), 0.52% (cyan), 0.74%
(pink), 0.93% (green), 1.57% (orange) c) Idye/Iligand of truMOF-1
as a function of dye loading level, together with simulated values
from the NNH model and the model including JBNN d) Idye/Iligand
of dye@truMOF-2 as a function of dye loading level, together
with simulated values from the NNH model and the model includ-
ing JBNN
Figure 6. a) Time-resolved emission traces of dye@truMOF-1
with a dye loading level of 0.12% [truMOF (black): ex@339nm
em@385nm; Energy Transfer (blue): ex@375nm, em@485nm;
Dye(cyan):ex@455nm, em@495nm] and control sample of
truMOF-1 without dye (red): ex@339nm em@400nm. Noise has
been removed in the deconvolution routine; b) Time-resolved
emission traces of truMOF-1 with different dye doping levels
(excited at 375 nm and detected at 485nm).
We systematically changed the excitation wavelength to collect
emission spectra and assembled them into the 2D map shown in
Fig. 5. On the map, the vertical axis represents the excitation
wavelength and the horizontal axis represents the emission wave-
length. The energy transfer is easily identified on the 2D map as a
“cross-peak” (ex = 370 nm; em = 485 nm) between the two peaks
associated with ligand ex/em (ex = 370 nm ; em = 395 nm) and
dye ex/em (ex = 445 nm; λem=485 nm), as a result of exciting at
the ligand wavelength but emitting at the dye wavelength due to
energy transfer.
Time-Resolved Emission Measurements and Exciton Migra-
tion
Time-resolved emission measurements were used to delineate
the underlying dynamics of exciton migration and energy transfer.
The intensities of the time-resolved emission for the ligand and
the dye are proportional to their excited state populations as a
function of time, and can be obtained after deconvolution of the
excitation pulse from the recorded curves (Fig. 6, Fig. S22&23
and Table S3). Even for the very short lifetime of the ligand dur-
ing energy transfer, a confident result with signal/noise > 5 can be
obtained. The coumarin emission rises in the beginning with the
decrease of the ligand emission on the timescale of ligand lifetime,
and then goes back to ground state by emissive transition and non-
emissive relaxation at the dye lifetime. The existence of this initial
growth period again confirms the energy transfer from the ligand
to the dye.
The shortened emission lifetime of the ligand after dye loading
is consistent with a diffusional quenching mechanism for the lig-
and-to-dye energy transfer, as compared to static quenching. The
major difference between these two quenching modes is that the
relative distance between the emitter and the quencher changes in
the diffusional quenching on the timescale of the excited state
lifetime, while this distance does not change in static quenching.
In the dye@MOF hybrid, the physical distance between the ligand
(emitter) and the dye (quencher) does not change on the time scale
of ligand lifetime, but the excited state can migrate on the frame-
work through multiple ligand-to-ligand energy transfer. This exci-
ton migration changes the relative distance between the excited
state and the dye acceptor, thus effectively creating conditions for
Figure 5. 2D fluorescence spectra of the dye@truMOF-1 assem-
bly at different dye loading levels: a) 0% b) 0.24% c) 0.42% d)
0.98%
This energy transfer peak becomes more visible as higher
amounts of coumarin dye were loaded into the MOFs (Fig. 4b).
As the dye concentration increases to 0.98%, the truxene ex/em
ACS Paragon Plus Environment

Journal of the American Chemical Society
Page 4 of 8
diffusional quenching that leads to the same mathematical conse-
perimental absorption and emission spectra of the donor and ac-
ceptor by
1
2
3
4
quences as molecular diffusion. The exciton migration greatly
enhances the energy transfer efficiency and is widely used by
light-harvesting systems in natural photosynthesis, as well as in
artificial systems for amplified quenching-based fluorescent de-
tection.10
∞퐹퐷(휆)휀퐴(휆)휆4푑휆
∫
0
J =
(eq. 2)
휀
ℏc ∞퐹 (휆)휆3푑휆
(휆)푑휆
퐴
휆
∫
∫
퐷
0
where 퐹퐷(휆) and 휀퐴(휆) are the experimental emission spectrum of
the donor and absorption spectrum of the acceptor, respectively.
5
6
7
8
9
The exciton coupling can be evaluated by columbic coupling
between the excited states of the donor and acceptor when wave-
function overlap between the two is negligible as in the MOF
structure. We estimated this columbic coupling using atomic tran-
sition densities,40,57-59 which yields much more reliable results
than the point dipole approximation at short ligand-ligand dis-
tances.
Simulation of Exciton Dynamics
The above measurements and analyses showed that energy
transfer in truMOF-2 is more efficient than that in truMOF-1. As
the two MOFs were constructed from the same ligands and the
same metal ions, the difference must result from their structures.
To understand the relationship between structure and energy
transfer and develop a principle for designing light-harvesting
materials, we performed simulations of exciton dynamics in these
systems.
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
푞푖푡푞푗푡
(푅푖푚−푅푗푙)
1
푁푚 푁푙
푖
∑
∑
푗
V푚푙
=
(eq. 3)
4휋휖0
where 푞푖푡 and 푅푖푚 are the atomic transition density and position of
the atom i in the molecule m.
The rate of energy transfer for singlet excitons can be described
by the Förster energy transfer theory (but beyond the point-dipole
approximation, see below).40,57-59 With crystal structures, energy
transfer rates were obtained between every two ligands in a 7×7×7
cube containing 343 unit-cells and 5488 L ligands for truMOF-1,
or 2744 L ligands for truMOF-2.
These coupling values are different in truMOF-1 and truMOF-2.
In truMOF-1, the adjacent ligands in the same tetrahedral cage are
very close to each other with inter-ligand coupling of 349 cm-1.
The couplings between ligands in different cages are much small-
er, with the largest value of 123 cm-1. In truMOF-2, the coupling
between closest ligands is only 166 cm-1, a value much smaller
than the largest one in truMOF-1, but energy transport in truMOF-
2 is more efficient than that in truMOF-1. This is because ligands
in truMOF-2 are more connected while ligands in truMOF-1 form
more isolated cages. This illustrates the importance of topology in
addition to inter-ligand coupling in dictating the efficiency of
energy transfer.
We first used the nearest neighbor approximation, considering
exciton hopping only between ligands with a center-to-center
distance of less than 2.0 nm (nearest neighbors). The simulations,
however, significantly underestimated the energy transfer effi-
ciency of truMOF-1 compared to the experimental results. After
adding back the energy transfer over longer distances, reasonable
energy transfer efficiencies were obtained. The contributions from
exciton jumping beyond the nearest neighbor account for 67% of
the energy transfer rates for truMOF-1 as shown in Fig. 4.
The atomic transition densities were obtained from singly ex-
cited configuration interaction calculations based on an INDO
ground state wave-function. The oscillation strength f of the cal-
culated results were normalized to experimental absorption spec-
tra of the donor and acceptor by
Since the Förster energy transfer rate decreases with increasing
donor-acceptor separation in an r-6 relationship, the large propor-
tion of longer distance jumping is counterintuitive. Energy trans-
fer over twice the distance will thus be 26 or 64 times slower. Our
rate calculations in the simulations confirmed such a dependence
on distance. One-step jumping over twice the distance takes far
more time than two successive hops between nearest neighbors by
a factor of 32. One might thus conclude that long distance jump-
ing in energy transfer should be very limited and almost negligi-
ble.
f = 0.0429× 휀(휆) 푑휆 (eq. 4)
∫
휆2
For the L ligand with C3h symmetry, there are two degenerate
excited states with transition dipole moments in the molecular
plane. These two degenerate states transform as (x,y) under sym-
metry operations of the C3h point group and belongs to the E’
irreducible representation. The atomic transition density calcula-
tions considered the pair of excited states.
However, this argument does not take into account the expo-
nentially increased number of possible paths after adding jumps
over longer distances. Although each path has a small contribu-
tion to the overall rate, summation over all the possible paths
leads to a rate comparable to that of nearest neighbor hopping. We
present a simple model net of six molecules in the supporting
information (Section S7) to illustrate the large contribution of
multiple paths in long-distance energy transfer.
The calculated energy transfer rates between adjacent mole-
cules in the crystal structures are very different from those ob-
tained from point-dipole calculations, while the rates between
molecules separated by longer distances are very similar for these
two methods.
Solving the Model of Exciton Dynamics
Förster Energy Transfer Rate
Dye molecules were added to the structural model based on
calculated adsorption positions and distributions. The number of
added dye molecules was kept in accordance with the doping
level. The dye adsorption positions were predicted from an an-
nealing calculation with molecular force field using the Adsorber
Locater module in Materials Studio software suite, with the first
10 configurations with lowest energies selected. The occupancy
probabilities of all dye positions were assigned according to the
calculated adsorption energies following the Boltzmann distribu-
tion. The final dye molecules in the model were loaded by a ma-
chine-generated random number to the configurations with corre-
sponding occupancy probabilities. The calculations were per-
The traditional Förster resonance energy transfer (FRET) for-
mulation involves a point-dipole model. This point-dipole approx-
imation does not apply at a donor-acceptor separation of less than
2 nm. We thus used a more general Förster equation beyond the
point-dipole formulation in our simulation40,57-59
:
푘푡푟 = 2휋 푉2퐽 (eq. 1)
ℏ
where J is the overlap integral between the normalized absorption
spectrum of the acceptor and the emission spectra of the donor. V
is the exciton coupling between the acceptor and the donor.
The overlap integral, which arises from the energy conservation
requirement of the energy transfer, can be obtained from the ex-
ACS Paragon Plus Environment

)
(eq. 13)
(eq.7)
Page 5 of 8
Journal of the American Chemical Society
formed for several times with different dye distributions and then
sidered in different energy transport networks, we built a general
1
2
3
4
5
6
7
8
averaged to give the final simulation results.
isotropic model for exciton migration (see SI, Section S8). In this
model, we can tune the Förster energy transfer rate constants and
monitor the change of the percentage of contributions of JBNN in
the overall energy transfer events.
The exciton dynamics was then simulated using the master
equations:
푑
1
( )
( )
∑
∑
( )
푃 푡 = 푃 푡 {−
−
푗≠푖 푘푖,푗}+ 푗≠푖 푘푗,푖푃 푡
(eq. 5)
푖
푖
푗
푑푡
휏푖
The rate of Förster energy transfer in isotropic media with av-
eraged dipole orientations can be represented by a Förster distance
푅. When the donor and acceptor are separated by the Förster dis-
tance at random orientations, 50% of the donor energy will be
transferred to the acceptor. The Förster energy transfer rate is
or more concisely
푑
⃗
⃗
( )
( )
푑푡 푃 푡 = 퐾 푃 푡
(eq. 6)
⃗
( )
where 푃 푡 is the column vector describing excitation population
9
at each site including both the ligand molecules and the dye mole-
1 푅6
휏퐷 푟6
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
k퐹 =
(eq. 15)
cules. 퐾 is the rate matrix that is constructed from the lifetime
decay of the excited state on this site (1) and energy transfer with
where 휏퐷 is the donor lifetime and 푟 is the donor-acceptor separa-
tion.
휏푖
all the other sites (푘푖,푗 and 푘푗,푖).
As an example, the Förster energy transfer distance between the
L ligands in the truMOFs is 3.5 nm. For comparison, the adjacent
ligands in the MOFs are separated by only 0.87-1.8 nm in
truMOF-1 and 1.27 nm in truMOF-2. These Förster distances are
typical for organic dyes. In photosynthetic antennae in chloro-
plasts, the Förster distance between chlorophylls is 4.2-9.0
nm,47,49,60 and the separation between adjacent chlorophylls is
1~1.3 nm,47-49 which are comparable to the tru-MOFs.
The master equation was solved by propagating the site popula-
tions in time
⃗
⃗
( )
푃 푡 = exp
( )
(퐾푡) 푃 0
⃗⃗⃗
( )
where⁡푃 0 is the initial excited state populations, being set to
unity on all ligand molecules and zero on all dye molecules.
( )
The time-dependent emission intensities of the ligand I퐿 t and
( )
the dye I퐷 t can be calculated from the excited state populations
by knowing the fluorescence rate Γ, which are determined exper-
imentally from fluorescence lifetime 휏 and quantum efficiency Φ.
In the simulation of general isotropic systems, the Förster dis-
tances (RLL and RLD) were normalized by the ligand-ligand sepa-
ration (rL). For simplification, the ligand-dye distance is set to the
same as the ligand-ligand separation in this model. The percent-
age of contributions from JBNN to Iligand/Idye was evaluated by
systematically changing RLL/rL and RLD/rL as shown in Fig. 7 (see
Section S8 in [SI] for more details).
Γ = Φ휏 (eq. 8)
( )
I퐿 t = Γ퐿 ∙P
( )
푡
and
(eq. 9)
퐿푖푔푎푛푑
( )
I퐷 t = α ∙Γ퐷 ∙푃퐷푦푒(푡)
(eq. 10)
The total emission intensities of the ligand and the dye can be
Contributions of JBNN increase with a faster ligand-to-ligand
energy transfer rate (larger RLL/rL) and decrease with a faster lig-
and-to-dye energy transfer rate (larger RLD/rL). This result is ra-
tionalized as the long distance jumping mainly affects exciton
migration. With a lower ligand-to-dye energy transfer rate, the
excitons have more time to migrate on the framework before be-
ing transferred to the dye. Similarly, a higher ligand-to-ligand
energy transfer rate produces excitons with higher mobility. The
contribution of JBNN to the energy transfer is thus affected by
both the ligand-to-dye and ligand-to-ligand energy transfer rates,
and plays a significant role in a wide range of combinations of
these two parameters.
calculated as
∞
( )
I퐿 t 푑푡 (eq. 11)
I푙푖푔푎푛푑
=
∫
0
∞
=
∫
0
( )
I퐷 t 푑푡 (eq. 12)
I푑푦푒
Diffusivity of Excitons
The diffusivity of the excitons can be evaluated by putting one
exciton at the center of the crystalline model, and monitor how
this exciton diffuse outward.
Diffusion from a point source in an infinite homogeneous vol-
ume can be estimated by
1
푟2
(− 4퐷푡
( )
P r,t = 4휋퐷푡 exp
1.000
0.897
0.795
0.692
0.589
0.486
0.384
0.281
0.178
0.281
0.384
6
5
4
3
2
0.486
where D is the diffusivity of the exciton.
0.692
0.795
By fitting the simulations to the above formula, the diffusivities
were determined to be 1.8×10-2 cm2/s and 2.3×10-2 cm2/s for
truMOF-1 and truMOF-2, respectively. These numbers are rela-
tively large compared to typical values in hetero-junction organic
solar cells.15 The exciton migration distances can be estimated by
considering a random walk of the exciton in 3D within its lifetime:
0.589
0.897
L = 퐷휏
(eq. 14)
√
The exciton migration distance is calculated to be 43 nm for
truMOF-1 and 48 nm for truMOF-2. Importantly, if only consid-
ering the nearest neighbor contributions, these migration distances
will be reduced to 20 nm in truMOF-1 and 25 nm in truMOF-2.
The jumping beyond nearest neighbor thus increases this distance
by 115% in truMOF-1 and 92% in truMOF-2.
2
3
4
5
6
RLL/rL
Figure 7. The fraction of JBNN (Jump Beyond Nearest Neighbor)
in the overall energy transfer rates as a function of normalized
Förster distances RLL/rL (ligand-to-ligand) and RLD/rL (ligand-to-
Jumping Beyond Nearest Neighbor in General Cases
The JBNN can also be significant in other systems besides
these truMOFs. To investigate when the JBNN needs to be con-
ACS Paragon Plus Environment

Journal of the American Chemical Society
Page 6 of 8
dye) for dye doping level of 0.5%. The fraction of JBNN is repre-
Synthesis of truMOF-2: A mixture of Zn(NO3)2•4H2O (60 mg)
1
2
3
4
5
6
7
8
sented by colors on the map with contour lines showing the values.
and H3L (45 mg) were placed in a mixed solution of DMF (10 mL)
and CH3OH (0.3 mL), with several glass slides in a screw-capped
vial, and placed in a 90℃ oven for 2 days. The crystals grew on
the glass slides and the slides with crystals were taken out of the
solution and thoroughly washed with DMF and EtOH before other
experiments.
Conclusion
We studied the Förster energy transport of singlet excitons in
two light-harvesting MOFs built from truxene-based ligands. Both
these antenna frameworks efficiently transfer energy to coumarin
dye molecules loaded inside the MOF cavity. These systems re-
semble photosynthetic networks that funnel energy collected by
chlorophyll/bacteriochlorophyll arrays to their embedded reaction
centers. We found that efficient energy transfer and exciton mi-
gration in the MOF system could not be quantitatively explained
using the usual step-by-step random hopping model adopted in
previous MOF energy transfer analyses. Exciton jumping beyond
nearest neighbors was found to account for up to 67% of the ener-
gy transfer rates in these systems with singlet excited states. Our
work thus presents a significant insight that will shape the design
of efficient energy transport networks.
9
ASSOCIATED CONTENT
Supporting Information
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Ligand Synthesis, Powder X-ray Diffractions, Thermogravimetric
Analysis, Fluorescence and UV-Vis Spectra, Model Network,
Exciton Dynamics Simulation. This material is available free of
charge via the Internet at http://pubs.acs.org.
AUTHOR INFORMATION
Corresponding Author
Experimental Section
E-mail: wangchengxmu@xmu.edu.cn
2, 7, 12-tribromo-5, 5', 10, 10', 15, 15'-hexaethyltruxene was syn-
thesized according to the literature.61
Present Addresses
‡
⁡Key Laboratory of Polyoxometalate Science of the Ministry of
Synthesis of 5, 5΄, 10, 10΄, 15, 15΄ -hexaethyltruxene-2,7,12–tri-
benzoate methyl ester (Me3L): A mixture of 2, 7, 12-tribromo-5,
5', 10, 10', 15, 15'-hexaethyltruxene (408 mg, 0.6 mmol), 4-
(methoxycarbonyl)phenylboronic acid (446 mg, 2.4 mmol),
Pd[P(C6H5)3]4 (150 mg, 0.13 mmol), K2CO3 (1.4 g), THF (20 mL),
and H2O (5 mL) was placed into a 100 mL sealed container with a
magnetic stirring bar and evacuated and purged with nitrogen.
Then the mixture was heated to 100℃ under nitrogen protection
for 3 days. After the mixture was cooled to room temperature, the
solvent was removed with a rotary evaporator. The crude product
was purified by column chromatography to obtain the pure prod-
uct (150 mg. 27.3% yield). 1H NMR (400 MHz, CDCl3) δ 8.46 (d,
J = 8.1 Hz, 3H), 8.17 (d, J = 8.0 Hz, 6H), 7.82 (d, J = 8.2 Hz, 6H),
7.72 (d, J = 8.4 Hz, 6H), 3.98 (s, 9H), 3.09 (dd, J = 13.8, 7.2 Hz,
6H), 2.27 (dd, J = 13.7, 7.2 Hz, 6H), 0.30 (t, J = 7.1 Hz, 18H).
Education, Faculty of Chemistry, Northeast Normal University,
Changchun, Jilin 130024, P.R. China
Author Contributions
†These authors contributed equally.
Notes
The authors declare no competing financial interests.
ACKNOWLEDGMENT
We thank the National Natural Science Foundation of P.R. China
(21471126), the National Thousand Talents Program of the P.R.
of China (to C.W. and W.L.), and the 985 Program of Chemistry
and Chemical Engineering disciplines of Xiamen University for
support with funding. Single crystal diffraction studies were per-
formed at ChemMatCARS, APS, Argonne National Laboratory
(ANL), which is principally supported by the National Science
Foundation (NSF/CHE-1346572). XAS analysis was performed at
Beamline 9-BM, APS, ANL. Use of the APS, an Office of Sci-
ence User Facility operated for the U.S. Department of Energy
(DOE) Office of Science by Argonne National Laboratory, was
supported by the U.S. DOE under Contract No. DE-AC02-
06CH11357. We also thank Prof. Xiaoyu Cao and Dr. Xuefu Hu
for help with the ligand synthesis.
Synthesis of 5, 5΄, 10, 10΄, 15, 15΄ -hexaethyltruxene-2,7,12–tri-
benzoic acid (H3L): 5, 5΄, 10, 10 ', 15, 15΄-hexaethyltruxene-
2,7,12-tribenzoate methyl ester (200 mg, 0.36 mmol) was dis-
solved in a mixture of THF (10 mL), EtOH (10 mL), and 6 M
aqueous NaOH solution (10 mL). The mixture was heated to 80
oC and refluxed for 8 h. After the mixture was cooled to room
temperature, the organic solvents were removed by a rotary evap-
tor. The aqueous solution of the solid was adjusted to pH<1 to
precipitate the product which was washed with H2O several times
(180 mg, 94% yield). 1H NMR (400 MHz, DMSO): δ 8.46 (d, J =
8.4 Hz, 3H), 8.09 (d, J = 8.4 Hz, 6H), 7.99 (d, J = 8.5 Hz, 9H),
7.89 (d, J = 7.3 Hz, 3H), 3.02 (dd, J = 13.2, 6.8 Hz, 6H), 2.36 (dd,
J = 13.5, 7.0 Hz, 6H), 0.25 – 0.08 (m, 18H). 13C NMR (126 MHz,
DMSO): δ 167.70, 153.66, 144.61, 144.55, 140.34, 138.60,
138.02, 130.49, 129.99, 127.35, 126.26, 125.21,121.23, 57.15,
29.15, 8.94. Elemental analysis: Anal. Calc.: C 82.73%, H 6.25 %.
Found: C 79%, H 6.3 %.)
REFERENCES
(1) Cheng, Y.-C.; Fleming, G. R. Ann. Rev. Phys. Chem. 2009, 60,
241.
(2) Amerongen, H. v.; Grondelle, R. v.; Valkunas, L. In
Photosynthetic Excitons; WORLD SCIENTIFIC: 2011, p 1.
(3) Grover, M.; Silbey, R. J. Chem. Phys. 1971, 54, 4843.
(4) Van Zandvoort, M.; Wróbel, D.; Lettinga, P.; Ginkel, G. v.;
Levine, Y. K. Photochem. & Photobio. 1995, 62, 279.
(5) Devenney, M.; Worl, L. A.; Gould, S.; Guadalupe, A.;
Sullivan, B. P.; Caspar, J. V.; Leasure, R. L.; Gardner, J. R.;
Meyer, T. J. J. Phys. Chem. A 1997, 101, 4535.
(6) Gilat, S. L.; Adronov, A.; Frechet, J. M. J. Angew. Chem., Int.
Ed. 1999, 38, 1422.
Synthesis of truMOF-1: A mixture of Zn(NO3)2•4H2O (60 mg)
and H3L (45 mg) were placed in a mixed solution of DMF (10
mL), CH3OH (0.3 mL) and H2O (0.3 mL), with several glass
slides in a screw-capped vial, and placed in a 90℃ oven for 2
days. The crystals grew on the glass slides and the slides with
crystals were taken out of the solution and thoroughly washed
with DMF and EtOH before other experiments.
(7) Ward, M. D.; Barigelletti, F. Coord. Chem. Rev. 2001, 216–
217, 127.
ACS Paragon Plus Environment

Page 7 of 8
Journal of the American Chemical Society
(8) Odobel, F.; Massiot, D.; Harrison, B. S.; Schanze, K. S.
(37) Kent, C. A.; Mehl, B. P.; Ma, L.; Papanikolas, J. M.; Meyer,
1
2
3
4
5
6
7
8
Langmuir 2003, 19, 30.
T. J.; Lin, W. J. Am. Chem. Soc. 2010, 132, 12767.
(38) Kent, C. A.; Liu, D.; Ma, L.; Papanikolas, J. M.; Meyer, T. J.;
Lin, W. J. Am. Chem. Soc. 2011, 133, 12940.
(39) Lee, C. Y.; Farha, O. K.; Hong, B. J.; Sarjeant, A. A.;
Nguyen, S. B. T.; Hupp, J. T. J. Am. Chem. Soc. 2011, 133, 15858.
(40) Son, H. J.; Jin, S.; Patwardhan, S.; Wezenberg, S. J.; Jeong,
N. C.; So, M.; Wilmer, C. E.; Sarjeant, A. A.; Schatz, G. C.; Snurr,
R. Q.; Farha, O. K.; Wiederrecht, G. P.; Hupp, J. T. J. Am. Chem.
Soc. 2013, 135, 862.
(41) Kent, C. A.; Liu, D.; Ito, A.; Zhang, T.; Brennaman, M. K.;
Meyer, T. J.; Lin, W. J. Mater. Chem. A 2013, 1, 14982.
(42) So, M. C.; Jin, S.; Son, H.-J.; Wiederrecht, G. P.; Farha, O.
K.; Hupp, J. T. J. Am. Chem. Soc. 2013, 135, 15698.
(43) Jin, S.; Son, H.-J.; Farha, O. K.; Wiederrecht, G. P.; Hupp, J.
T. J. Am. Chem. Soc. 2013, 135, 955.
(44) Lin, J.; Hu, X.; Zhang, P.; Van Rynbach, A.; Beratan, D. N.;
Kent, C. A.; Mehl, B. P.; Papanikolas, J. M.; Meyer, T. J.; Lin, W.;
Skourtis, S. S.; Constantinou, M. J. Phys. Chem. C 2013, 117,
22250.
(45) Maza, W. A.; Ahrenholtz, S. R.; Epley, C. C.; Day, C. S.;
Morris, A. J. J. Phys. Chem. C 2014, 118, 14200.
(46) Maza, W. A.; Padilla, R.; Morris, A. J. J. Am. Chem. Soc.
2015, 137, 8161.
(47) Byrdin, M.; Jordan, P.; Krauss, N.; Fromme, P.; Stehlik, D.;
Schlodder, E. Biophys. J. 2002, 83, 433.
(48) Liu, Z.; Yan, H.; Wang, K.; Kuang, T.; Zhang, J.; Gui, L.; An,
X.; Chang, W. Nature 2004, 428, 287.
(49) Pålsson, L. O.; Spangfort, M. D.; Gulbinas, V.; Gillbro, T.
FEBS Lett. 1994, 339, 134.
(50) Renger, T.; May, V.; Kuhn, O. Phys. Rep. 2001, 343, 137.
(51) Tamiaki, H.; Shibata, R.; Mizoguchi, T. Photochem. &
Photobio. 2007, 83, 152.
(52) Kent, C. A.; Liu, D.; Meyer, T. J.; Lin, W. J. Am. Chem. Soc.
2012, 134, 3991.
(53) Murata, N.; Araki, S.; Fujita, Y.; Suzuki, K.; Kuwabara, T.;
Mathis, P. Photosynth. Res. 1986, 9, 63.
(54) Noy, D.; Moser, C. C.; Dutton, P. L. Biochim. Biophys. Acta-
Bioenergetics 2006, 1757, 90.
(55) van Grondelle, R. Biochim. Biophys. Acta- Bioenergetics
1985, 811, 147.
(56) The ligand in MOF structure has absorption maximum at 370
nm while free acid ligand has absorption maximum at 333 nm.
(57) Wong, K. F.; Bagchi, B.; Rossky, P. J. J. Phys. Chem. A
2004, 108, 5752.
(58) Howard, I. A.; Zutterman, F.; Deroover, G.; Lamoen, D.;
Van Alsenoy, C. J. Phys. Chem. B 2004, 108, 19155.
(59) Patwardhan, S.; Sengupta, S.; Würthner, F.; Siebbeles, L. D.
A.; Grozema, F. J. Phys. Chem. C 2010, 114, 20834.
(60) Şener, M.; Strümpfer, J.; Hsin, J.; Chandler, D.; Scheuring,
S.; Hunter, C. N.; Schulten, K. ChemPhysChem 2011, 12, 518.
(61) Yuan, M.-S.; Wang, D.-E.; Li, T.-B.; Xu, Y.; Wang, W.-J.;
Tu, Q.; Zhang, Y.; Li, M.; Wang, J. Dyes & Pigments 2014, 107,
60.
(9) Higgins, G. T.; Bergeron, B. V.; Hasselmann, G. M.; Farzad,
F.; Meyer, G. J. J. Phys. Chem. B 2006, 110, 2598.
(10) Thomas, S. W., III; Joly, G. D.; Swager, T. M. Chem. Rev.
2007, 107, 1339.
(11) Aratani, N.; Kim, D.; Osuka, A. Acc. Chem. Res. 2009, 42,
1922.
(12) Wasielewski, M. R. Acc. Chem. Res. 2009, 42, 1910.
(13) Andrew, T. L.; Swager, T. M. J. Polym. Sci. B-Polym. Phys.
2011, 49, 476.
(14) Chen, L.; Furukawa, K.; Gao, J.; Nagai, A.; Nakamura, T.;
Dong, Y.; Jiang, D. J. Am. Chem. Soc. 2014, 136, 9806.
(15) Menke, S. M.; Holmes, R. J. Energ. Environ. Sci. 2014, 7,
499.
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
(16) Cui, Y.; Yue, Y.; Qian, G.; Chen, B. Chem. Rev. 2012, 112,
1126.
(17) Zhang, T.; Lin, W. Chem. Soc. Rev. 2014, 43, 5982.
(18) Hu, Z.; Deibert, B. J.; Li, J. Chem. Soc. Rev. 2014, 43, 5815.
(19) So, M. C.; Wiederrecht, G. P.; Mondloch, J. E.; Hupp, J. T.;
Farha, O. K. Chem. Commun. 2015, 51, 3501.
(20) Zhang, X.; Wang, W.; Hu, Z.; Wang, G.; Uvdal, K. Coord.
Chem. Rev. 2015, 284, 206.
(21) O'Keeffe, M.; Eddaoudi, M.; Li, H. L.; Reineke, T.; Yaghi, O.
M. J. Solid State Chem. 2000, 152, 3.
(22) Ferey, G.; Mellot-Draznieks, C.; Serre, C.; Millange, F. Acc.
Chem. Res. 2005, 38, 217.
(23) Inokuma, Y.; Kawano, M.; Fujita, M. Nat. Chem. 2011, 3,
349.
(24) Herm, Z. R.; Wiers, B. M.; Mason, J. A.; van Baten, J. M.;
Hudson, M. R.; Zajdel, P.; Brown, C. M.; Masciocchi, N.;
Krishna, R.; Long, J. R. Science 2013, 340, 960.
(25) Shustova, N. B.; McCarthy, B. D.; Dincă, M. J. Am. Chem.
Soc. 2011, 133, 20126.
(26) An, J.; Shade, C. M.; Chengelis-Czegan, D. A.; Petoud, S.;
Rosi, N. L. J. Am. Chem. Soc. 2011, 133, 1220.
(27) Liu, Y.; Pan, M.; Yang, Q.-Y.; Fu, L.; Li, K.; Wei, S.-C.; Su,
C.-Y. Chem. Mater. 2012, 24, 1954.
(28) Williams, D. E.; Rietman, J. A.; Maier, J. M.; Tan, R.;
Greytak, A. B.; Smith, M. D.; Krause, J. A.; Shustova, N. B. J.
Am. Chem. Soc. 2014, 136, 11886.
(29) Yu, J.; Cui, Y.; Xu, H.; Yang, Y.; Wang, Z.; Chen, B.; Qian,
G. Nat. Commun, 2013, 4.
(30) Cui, Y.; Song, R.; Yu, J.; Liu, M.; Wang, Z.; Wu, C.; Yang,
Y.; Wang, Z.; Chen, B.; Qian, G. Adv. Mater. 2015, 27, 1420.
(31) Dong, M.-J.; Zhao, M.; Ou, S.; Zou, C.; Wu, C.-D. Angew.
Chem., Int. Ed. 2014, 53, 1575.
(32) Park, J.; Feng, D.; Yuan, S.; Zhou, H.-C. Angew. Chem., Int.
Ed. 2015, 54, 430.
(33) Yanai, N.; Kitayama, K.; Hijikata, Y.; Sato, H.; Matsuda, R.;
Kubota, Y.; Takata, M.; Mizuno, M.; Uemura, T.; Kitagawa, S.
Nat. Mater. 2011, 10, 787.
(34) Lan, A.; Li, K.; Wu, H.; Olson, D. H.; Emge, T. J.; Ki, W.;
Hong, M.; Li, J. Angew. Chem., Int. Ed. 2009, 48, 2334.
(35) Foster, M. E.; Azoulay, J. D.; Wong, B. M.; Allendorf, M. D.
Chem. Sci. 2014, 5, 2081.
(36) Zhang, X.; Ballem, M. A.; Hu, Z.-J.; Bergman, P.; Uvdal, K.
Angew. Chem., Int. Ed. 2011, 50, 5729.
ACS Paragon Plus Environment

Journal of the American Chemical Society
Page 8 of 8
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Förster Energy Transport in Metal-Organic Frameworks Is Beyond Step-by-Step Hopping
8
ACS Paragon Plus Environment